Abstract
It has been shown earlier that while strict localization of the free Dirac particle is not describable within the usual mathematical formalism, it is possible to describe sequences of positive-energy states whose spread Δ x =〈(x−x 0)2〉 about any given point x 0 approaches zero, where x is Dirac's position operator. The concept of a generalized function is extended here to allow for the succinct description of localized states in terms of “Asymptotic Localizing Functions.” Localization of both the nonrelativistic particle and the Dirac particle can be adequately represented in this new formalism.
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Melloy, G.F. The Generalized Representation of Particle Localization in Quantum Mechanics. Foundations of Physics 32, 503–530 (2002). https://doi.org/10.1023/A:1015080215317
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DOI: https://doi.org/10.1023/A:1015080215317